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22.4 Clocks in Motion: Examples
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Module 22: Clocks in Motion: Examples Problem 1

Let’s consider the example from lecture of observers on a moving train firing paint splotches on the ground. Recall that those on the train fired the paint splotches simultaneously from their perspective, but those on the platform said the rear paint was fired first, the train continued to move, and only some time later did the front paint fire. This is how the platform observers explain how the train observers claim a longer length for the train. Let’s now consider this example quantitatively.

  1. 1. Question

    From the perspective of an observer on the platform, how much time elapses between the moment the rear splotch is deposited and when the front splotch is deposited? Give your answer in terms of the speed of the train vv, and the resting length of the train, L0L_0.

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  2. 2. Question

    From the perspective of an observer on the platform, how far does the train move in the interval between when the first and second splotches are painted?

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  3. 3. Question

    Using the result in the previous parts, calculate the distance between the two paint splotches from the perspective of an observer on the platform.

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